Control of Valence-Band Hole Spin by Electric Field

Coherent properties of the hole spin in an electric field are investigated. The tunneling between valence bands is used to control the transitions between the spin states. Extensive numerical studies using the time-dependent Schrödinger equation for valence band are presented to demonstrate the characteristic properties of the hole spin dynamics in dc, harmonic, as well as optimized electric fields for real valence bands of silicon. The paper also shows how one can connect the average hole spin with the initial hole wave function in the time-dependent Schrödinger equation.